plasticity

In conventional elastic-plastic constitutive models for clays, elastic strains are usually calculated by isotropic hypo-elastic models. However, this class of elasticity has two major deficiencies: (a) it ignores the influence of shear stress-induced anisotropy and; (b) it does not conserve energy. Another class of the elasticity theory, the so-called hyper-elasticity theory, is capable of eliminating both deficiencies simultaneously. In this study, constitutive equations of a recently proposed elastic-plastic platform for clays named SANICLAY are generalized in order to enable it to consider the possibility of the anisotropic response in the elastic domain. The generalized formulation allows shear-volumetric coupling not existing in the basic platform. Then, the elastic moduli obtained from a hyper-elastic model are implemented within the generalized SANICLAY formulation. The refined model predictions are directly compared with the experimental data of various clays. It is shown that more realistic stress paths are achieved from the refined model.

Integrating the rate form equations governing the behavior of material is an important step in solving every plasticity problem. Providing a compromise between accuracy and computational effort demands the combination of low order elements with efficient integration algorithms. First and second order accurate integration algorithms are well established in the realm of infinitesimal theory. However for large deformation plasticity models, second order integration algorithms are not given much attention in the literature. Inspired by midpoint rule algorithms conventionally used in small deformations, a new integration algorithm is proposed for finite strain J2 plasticity that outperforms the classical backward Euler method. Algorithmic setup as well as the derivation of tangent operator which is crucial for quadratic rate of convergence of the Newton-Raphson algorithm is discussed in detail. Employing four node quadrilateral elements in solving benchmark examples it is shown that the proposed algorithm is very stable from numerical standpoint and has outstanding convergence properties.

In this work a double step algorithm is presented for the integration of equations governing the behavior of von Mises material in plastic limit. The isotropic and kinematic hardenings employed are of general type and the evolution of back stress follows the Armstrong–Frederick rule. Theoretical and numerical aspects are discussed in detail and a comparison is made with the classical backward Euler method.